Weight-averaged mean

A variant of the concept of Cardenas and O Driscoll is the approach of Marten and Hamielec [40]. According to these authors, k, is proportional to the difusion coefficients, which are a function of the viscosity of the medium. This viscosity depends on the weight average mean molecular mass and thus kt can be written as... 

Droplet-size distributions and average droplet sizes (volume-surface mean diameter d32 and weighted average mean diameter d43) of O/W emulsions were... 

The National Institute of Occupational Safety and Health (NIOSH) estimates that 90 percent of noise-exposed workers in the United States are exposed to 95 dB of TWA (time-weighted average), meaning they need only 10 dB of protection or attenuation. Workers who are overprotected from the noise exposure may feel they may not hear communications properly and might not be safe. There are no U.S. standards for overprotection for noise exposure however, European guidance, EN 458, states that workers attenuated noise levels should be no lower than 75-84 dB for ideal communication in noise (Table N.2). 

The susceptibility tensors give the correct relationship for the macroscopic material. For individual molecules, the polarizability a, hyperpolarizability P, and second hyperpolarizability y, can be defined they are also tensor quantities. The susceptibility tensors are weighted averages of the molecular values, where the weight accounts for molecular orientation. The obvious correspondence is correct, meaning that is a linear combination of a values, is a linear combination of P values, and so on. 

To determine the average porosity of a homogeneous but nonuniform medium, the correct mean of the distribution of porosity must be evaluated. The porosities of natural and artificial media usually are normally distributed. The average porosity of a heterogeneous nonuniform medium is the volume-weighted average of the number average ... 

This means that the average permeability for this heterogeneous medium is the area-weighted average of the average permeability of each of the elements. If the permeability of each element is log-normally distributed, these are the geometric means. 

The weight average molecular weight is important elsewhere in the interpretation of polymer properties hence its relationship to other averages deserves careful inspection. The mean-square molecular weight is, of course,... 

At the critical point ac=(/—1) S Xn is finite, which signifies merely that the number of molecules is by no means zero the weight average, however, is infinite at ac and, of course, the ratio of Xw to Xn is infinite, indicating extreme heterogeneity. 

Fig. 4.3. (A) Composite multispecies benthic foraminiferal Mg/Ca records from three deep-sea sites DSDP Site 573, ODP Site 926, and ODP Site 689. (B) Species-adjusted Mg/Ca data. Error bars represent standard deviations of the means where more than one species was present in a sample. The smoothed curve through the data represents a 15% weighted average. (C) Mg temperature record obtained by applying a Mg calibration to the record in (B). Broken line indicates temperatures calculated from the record assuming an ice-free world. Blue areas indicate periods of substantial ice-sheet growth determined from the S 0 record in conjunction with the Mg temperature. (D) Cenozoic composite benthic foraminiferal S 0 record based on Atlantic cores and normalized to Cibicidoides spp. Vertical dashed line indicates probable existence of ice sheets as estimated by (2). 3w, seawater S 0. (E) Estimated variation in 8 0 composition of seawater, a measure of global ice volume, calculated by substituting Mg temperatures and benthic 8 0 data into the 8 0 paleotemperature equation (Lear et al., 2000).

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